LPINNs propose multiplying the first hidden activation of a dense PINN by input-dependent localization functions, endowing first-layer units with receptive fields to improve optimization on long domains and for high-order operators without domain partitioning.
See LICENSE filePhysics-Informed Neural NetworksPINN EnhancementNeural Network Localization
This paper investigates using artificial neural networks as surrogate models for black-box optimization, enabling efficient optimization when analytical function descriptions are unavailable by obtaining objective values through numerical simulation.
See LICENSE fileBlack-Box OptimizationSurrogate ModelNeural Network
Proposes the Fractional Fourier Neural Operator (FrFNO) that embeds the analytic Mittag-Leffler propagator to address the computational challenge of memory-dependent time derivatives and nonlocal fractional Laplacians in fractional PDEs, enabling efficient surrogate modeling.
See LICENSE fileFractional PDENeural OperatorMittag-Leffler Function
Proposes a triply-scalable equivariant Gaussian process method that encodes symmetries while maintaining probabilistic predictions and uncertainty quantification for large-scale scientific computing.
See LICENSE fileGaussian ProcessEquivariant Neural NetworksUncertainty Quantification
A comprehensive benchmark dataset for training and evaluating neural PDE solvers, containing six standard tasks on regular grids, structured grids, and irregular geometries, used for unified evaluation in the ICML 2024 paper Transolver.
PhD course lecture notes from University of Bozen/Bolzano covering Physics Informed Neural Networks and Neural Operators with PyTorch implementation tutorials.
